Application of the Averaging Method to the Investigation of Nonlinear Wave Processes in Elastic Systems with Circular Symmetry

Abstract

We apply asymptotic methods of nonlinear mechanics (the Bogolyubov–Mitropol'skii averaging method) to the construction of approximate solutions of a system of nonlinear equations describing wave processes in elastic systems with circular symmetry. As an example, we study the dynamics of interaction of two flexural waves that propagate in a cylindrical shell under the conditions of free oscillations and periodic excitation.